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An ARIMA Supply Chain Model

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  • Kenneth Gilbert

    (Department of Statistics, Operations and Management Science, University of Tennessee, Knoxville, Tennessee 37996-0532)

Abstract

This paper presents a multistage supply chain model that is based on Autoregressive Integrated Moving Average (ARIMA) time-series models. Given an ARIMA model of consumer demand and the lead times at each stage, it is shown that the orders and inventories at each stage are also ARIMA, and closed-form expressions for these models are given. The paper also discusses the causes of the bullwhip effect, a phenomenon in which variation in demand produces larger variations in upstream orders and inventory. This discussion reveals how different modeling can lead to different insights because they make different assumptions about the cause of the bullwhip effect. These observations are used to develop managerial insights about reducing the bullwhip effect.

Suggested Citation

  • Kenneth Gilbert, 2005. "An ARIMA Supply Chain Model," Management Science, INFORMS, vol. 51(2), pages 305-310, February.
    • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:2:p:305-310
    DOI: 10.1287/mnsc.1040.0308
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    References listed on IDEAS

    as
    1. Hau L. Lee & Kut C. So & Christopher S. Tang, 2000. "The Value of Information Sharing in a Two-Level Supply Chain," Management Science, INFORMS, vol. 46(5), pages 626-643, May.
    2. Srinivasan Raghunathan, 2001. "Information Sharing in a Supply Chain: A Note on its Value when Demand Is Nonstationary," Management Science, INFORMS, vol. 47(4), pages 605-610, April.
    3. Yossi Aviv, 2003. "A Time-Series Framework for Supply-Chain Inventory Management," Operations Research, INFORMS, vol. 51(2), pages 210-227, April.
    4. Yossi Aviv, 2002. "Gaining Benefits from Joint Forecasting and Replenishment Processes: The Case of Auto-Correlated Demand," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 55-74, December.
    5. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    6. Frank Chen & Zvi Drezner & Jennifer K. Ryan & David Simchi-Levi, 2000. "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information," Management Science, INFORMS, vol. 46(3), pages 436-443, March.
    7. Yossi Aviv, 2001. "The Effect of Collaborative Forecasting on Supply Chain Performance," Management Science, INFORMS, vol. 47(10), pages 1326-1343, October.
    8. Arthur F. Veinott, Jr., 1965. "Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem," Management Science, INFORMS, vol. 12(3), pages 206-222, November.
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